Chapter 19, Problem 54A

a.

To determine

The effect of doubling the thickness of the soap film on the interference pattern.

Explanation of Solution

Introduction:

Thin film interference occurs when light wave reflects from the top surface of a film experience constructive or destructive superposition, with the light wave reflected from the bottom surface.

A thin film has a higher refractive index than air. When light reflects from the top surface of this film it undergoes a phase shift of one half wave length

For destructive interference two waves must be out of phase by one half of the wavelength or an odd multiple of $\pi$ .

For constructive interference the phase difference between the two waves will be an even multiple of $\pi$ .

Prior to increase there was constructive interference. As with the increase in thickness the phase difference becomes an odd multiple of $\pi$ , hence, there will be destructive interference.

Conclusion:

As with the increase in thickness the phase difference becomes an odd multiple of $\pi$ , hence, there will be destructive interference.

b.

To determine

The effect of increasing the thickness of the film, by half a wavelength of the light, on the interference pattern.

Explanation of Solution

Introduction:

Thin film interference occurs when light wave reflects from the top surface of a film experience constructive or destructive superposition, with the light wave reflected from the bottom surface.

A thin film has a higher refractive index than air. When light reflects from the top surface of this film it undergoes a phase shift of one half wave length

For destructive interference two waves must be out of phase by one half of the wavelength or an odd multiple of $\pi$ .

For constructive interference the phase difference between the two waves will be an even multiple of $\pi$ .

Prior to increase there was constructive interference. As with the increase in thickness by half a wavelength of the light, the phase difference becomes an even multiple of $\pi$ . Hence, there will be constructive interference.

Conclusion:

As with the increase in thickness by half a wavelength of the light, the phase difference becomes an even multiple of $\pi$ . Hence, there will be constructive interference.

c.

To determine

The effect of reducing the thickness of the soap film by, one quarter of a wavelength of the light, on the interference pattern.

Explanation of Solution

Introduction:

Thin film interference occurs when light wave reflects from the top surface of a film experience constructive or destructive superposition, with the light wave reflected from the bottom surface.

A thin film has a higher refractive index than air. When light reflects from the top surface of this film it undergoes a phase shift of one half wave length

For destructive interference two waves must be out of phase by one half of the wavelength or an odd multiple of $\pi$ .

For constructive interference the phase difference between the two waves will be an even multiple of $\pi$ .

Prior to increase there was constructive interference. As with decreasing the thickness of the film by one quarter of a wavelength of the light the phase difference becomes an odd multiple of $\pi$ , there will be destructive interference.

Conclusion:

As with decreasing the thickness of the film by one quarter of a wavelength of the light the phase difference becomes an odd multiple of $\pi$ , there will be destructive interference.